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39 m 29 x 10 Total Number of Full-Time Employees Total Number of Part-Time Employees 10 mo 10 10 Total Number of Full-Time Employees: Total Number of Part-Time Employees Ⓡ Total Cost - X10 X10 ya 0 and integer for 9, 10, 11 and/9, 10, 11, 12, 1, 2, 3 11 L Ⓡ (3 n ✪ no no b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. Total Cost: 950 950 n9 10 yo yo Y10 10 y10 c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. yo - Эл yil yil yuu yil ₁- y11 ₁² 12 y2₂ y12 y12 y12 ₁² 12 'n Ⓡ 'n . . . 'n 12 n n 'n 3. Ⓡ3₂ n n 3. -Select your answer - -Select your answer- -Select your answer -Select your answer Select your answer- -Select your answer Select your answer. -Select your answer Select your answer Ⓡ3 Ⓡ d) After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full-time and part-time employees required and the total cost under the revised optimal solution. of required, round your answers to the nearest whole number of your answer is zero enter"0" Time (10:00am-11:00 am) Time (11:00 am/Noon.) Time (Noon-1:00p.m.) Time (1:00 pm-2:00p.m.) Time (2:00 pm-3:00p.m.) Time (3:00 pm.-4:00p.m.) Time (4:00 pm-5:00p.m.) Time (3:00 pm.-6:00p.m.) Time (6:00 pm-7:00p.m.)

39 m 29 x 10 Total Number of Full-Time Employees Total Number of Part-Time Employees 10 mo 10 10 Total Number of Full-Time Employees: Total Number of Part-Time Employees Ⓡ Total Cost - X10 X10 ya 0 and integer for 9, 10, 11 and/9, 10, 11, 12, 1, 2, 3 11 L Ⓡ (3 n ✪ no no b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. Total Cost: 950 950 n9 10 yo yo Y10 10 y10 c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. yo - Эл yil yil yuu yil ₁- y11 ₁² 12 y2₂ y12 y12 y12 ₁² 12 'n Ⓡ 'n . . . 'n 12 n n 'n 3. Ⓡ3₂ n n 3. -Select your answer - -Select your answer- -Select your answer -Select your answer Select your answer- -Select your answer Select your answer. -Select your answer Select your answer Ⓡ3 Ⓡ d) After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full-time and part-time employees required and the total cost under the revised optimal solution. of required, round your answers to the nearest whole number of your answer is zero enter"0" Time (10:00am-11:00 am) Time (11:00 am/Noon.) Time (Noon-1:00p.m.) Time (1:00 pm-2:00p.m.) Time (2:00 pm-3:00p.m.) Time (3:00 pm.-4:00p.m.) Time (4:00 pm-5:00p.m.) Time (3:00 pm.-6:00p.m.) Time (6:00 pm-7:00p.m.)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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apter 13 Assignment Xm Hide Feedback xx Incorrect 8 Icon Key yo + xx9 x10 e to search X10 x10 + x10 X10 ✪x10 X10 + x10 Xir yj 20 and integer for/= 9, 10, 11 and j = 9, 10, 11, 12, 1, 2, 3 X10 x₁1 + X * *x11 X xx Problem 13-15 Algo (Solving Integer Optimization Problems with Excel Solver) ][ va + (b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. Total Cost: $ 950 × vo + yg + yg + 8 *** XX (c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. If your answer is zero enter "0". Total Number of Full-Time Employees: Total Number of Part-Time Employees: J' * V10 y10+ VID + Y10 y10+ Y10 y10 y10 y11 | y11 y12 (99+ 12+ V₁2+ y12 + y12 + V₁2+ y12 y12 + + Ⓡyz * X * X y3 y3 × X * 13 y3 3 ...p (d) After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full-time and part-time employees required and the total cost under the revised optimal solution. If required, round your answers to the nearest whole number. If your answer is zero enter "0". Total Number of Full-Time Employees: Total Number of Part-Time Employees: Total Cost: $ - Select your answer - Select your answer Select your answer - V - Select your answer Select your answer - V - Select your answer V Select your answer - V - Select your answer - V Select your answer V X X × X × X × X Time (10:00 a.m.-11:00 a.m.) Time (11:00 a.m.-Noon.) Time (Noon.-1:00 p.m.) Time (1:00 p.m.-2:00 p.m.) Time (2:00 p.m.-3:00 p.m.) Time (3:00 p.m.-4:00p.m.) Time (4:00 p.m.-5:00p.m.) Time (5:00 p.m.-6:00 p.m.) Time (6:00 p.m.-7:00 p.m.) ARD 74°F Haze > Save Hint(s) Check My Work Question 4 of 5 Submit Assignment for Grading 10:39 AM 2/23/2023 X A-Z بین A+ (2)
Transcribed Image Text:apter 13 Assignment Xm Hide Feedback xx Incorrect 8 Icon Key yo + xx9 x10 e to search X10 x10 + x10 X10 ✪x10 X10 + x10 Xir yj 20 and integer for/= 9, 10, 11 and j = 9, 10, 11, 12, 1, 2, 3 X10 x₁1 + X * *x11 X xx Problem 13-15 Algo (Solving Integer Optimization Problems with Excel Solver) ][ va + (b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. Total Cost: $ 950 × vo + yg + yg + 8 *** XX (c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. If your answer is zero enter "0". Total Number of Full-Time Employees: Total Number of Part-Time Employees: J' * V10 y10+ VID + Y10 y10+ Y10 y10 y10 y11 | y11 y12 (99+ 12+ V₁2+ y12 + y12 + V₁2+ y12 y12 + + Ⓡyz * X * X y3 y3 × X * 13 y3 3 ...p (d) After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full-time and part-time employees required and the total cost under the revised optimal solution. If required, round your answers to the nearest whole number. If your answer is zero enter "0". Total Number of Full-Time Employees: Total Number of Part-Time Employees: Total Cost: $ - Select your answer - Select your answer Select your answer - V - Select your answer Select your answer - V - Select your answer V Select your answer - V - Select your answer - V Select your answer V X X × X × X × X Time (10:00 a.m.-11:00 a.m.) Time (11:00 a.m.-Noon.) Time (Noon.-1:00 p.m.) Time (1:00 p.m.-2:00 p.m.) Time (2:00 p.m.-3:00 p.m.) Time (3:00 p.m.-4:00p.m.) Time (4:00 p.m.-5:00p.m.) Time (5:00 p.m.-6:00 p.m.) Time (6:00 p.m.-7:00 p.m.) ARD 74°F Haze > Save Hint(s) Check My Work Question 4 of 5 Submit Assignment for Grading 10:39 AM 2/23/2023 X A-Z بین A+ (2)
ons Problem 13-15 Algo (Solving Integer Optimization Problems with Excel Solver) The Northside Bank working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. On Fridays, the bank open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here. Time Time 9:00 a.m.-10:00 a.m. 2:00 p.m.-3:00 p.m. 10:00 a.m.-11:00 a.m. 3:00 p.m.-4:00p.m. 11:00 a.m.-Noon 4:00 p.m.-5:00p.m. Noon-1:00 p.m. 5:00 p.m.-6:00 p.m. 1:00 p.m.-2:00 p.m. 6:00 p.m.-7:00p.m. Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day). s.t. No. of Tellers x9 6 yo Osearch 5 7 11 9 *x10 (a) Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let x = number of full-time employees coming on duty at the beginning of hour i and yj = number of part-time employees coming on duty at the beginning of hour j.) If your answer is zero enter "0" and if the constant is "1" it must be entered in the box. Min X10 + X ✔x10 × x10 + X10 x10 X10 x10 + X10 + X10 No. of Tellers X10 + 6 *x11 7 17 5 *Yo x11 Xir yj z 0 and integer for i= 9, 10, 11 and j = 9, 10, 11, 12, 1, 2, 3 x11 + ⓇX11 x11 + yg + yg + y⁹ (b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. × Total Cost: $ 950 y10 y10 y10+ y10 V10 y10 + y10 y10+ y10 + y10 3y10+ HH + (c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. If your answer is zero enter "0". Total Number of Full-Time Employees: Total Number of Part-Time Employees: + y₁₁ + y₁1 + y₁₁ + y11 + 99+ y12 y12 + y12 + y12 + V₁2+ V₁2+ y12 y12 + 12+ y12 1 X₂ + y₁ + 0 √₂ + *√₂ + 3y₂ + *v₂ *v₂ 6 y3 y3 y3 - Select your answer Select your answer - V V3 V3 Select your answer Select your answer y3 - Select your answer V3 - Select your answer Select your answer Y3 V3 V ✓ Select your answer - V Select your answer y3 - Select your answer V V X x X X X X X X X Question 4 of 5 ▸ X Hint(s) Check My Work Time (9:00 a.m.-10:00 a.m.) Time (10:00 a.m.-11:00 a.m.) Time (11:00 a.m.-Noon.) Time (Noon.-1:00 p.m.) Time (1:00 p.m.-2:00 p.m.) Time (2:00 p.m.-3:00 p.m.) Time (3:00 p.m.-4:00 p.m.) Time (4:00 p.m.-5:00p.m.) Time (5:00 p.m.-6:00 p.m.) Time (6:00 p.m.-7:00p.m.) 74°F Haze 10:39 AM 2/23/2023 2 A-Z o بین O
Transcribed Image Text:ons Problem 13-15 Algo (Solving Integer Optimization Problems with Excel Solver) The Northside Bank working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. On Fridays, the bank open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here. Time Time 9:00 a.m.-10:00 a.m. 2:00 p.m.-3:00 p.m. 10:00 a.m.-11:00 a.m. 3:00 p.m.-4:00p.m. 11:00 a.m.-Noon 4:00 p.m.-5:00p.m. Noon-1:00 p.m. 5:00 p.m.-6:00 p.m. 1:00 p.m.-2:00 p.m. 6:00 p.m.-7:00p.m. Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day). s.t. No. of Tellers x9 6 yo Osearch 5 7 11 9 *x10 (a) Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let x = number of full-time employees coming on duty at the beginning of hour i and yj = number of part-time employees coming on duty at the beginning of hour j.) If your answer is zero enter "0" and if the constant is "1" it must be entered in the box. Min X10 + X ✔x10 × x10 + X10 x10 X10 x10 + X10 + X10 No. of Tellers X10 + 6 *x11 7 17 5 *Yo x11 Xir yj z 0 and integer for i= 9, 10, 11 and j = 9, 10, 11, 12, 1, 2, 3 x11 + ⓇX11 x11 + yg + yg + y⁹ (b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. × Total Cost: $ 950 y10 y10 y10+ y10 V10 y10 + y10 y10+ y10 + y10 3y10+ HH + (c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. If your answer is zero enter "0". Total Number of Full-Time Employees: Total Number of Part-Time Employees: + y₁₁ + y₁1 + y₁₁ + y11 + 99+ y12 y12 + y12 + y12 + V₁2+ V₁2+ y12 y12 + 12+ y12 1 X₂ + y₁ + 0 √₂ + *√₂ + 3y₂ + *v₂ *v₂ 6 y3 y3 y3 - Select your answer Select your answer - V V3 V3 Select your answer Select your answer y3 - Select your answer V3 - Select your answer Select your answer Y3 V3 V ✓ Select your answer - V Select your answer y3 - Select your answer V V X x X X X X X X X Question 4 of 5 ▸ X Hint(s) Check My Work Time (9:00 a.m.-10:00 a.m.) Time (10:00 a.m.-11:00 a.m.) Time (11:00 a.m.-Noon.) Time (Noon.-1:00 p.m.) Time (1:00 p.m.-2:00 p.m.) Time (2:00 p.m.-3:00 p.m.) Time (3:00 p.m.-4:00 p.m.) Time (4:00 p.m.-5:00p.m.) Time (5:00 p.m.-6:00 p.m.) Time (6:00 p.m.-7:00p.m.) 74°F Haze 10:39 AM 2/23/2023 2 A-Z o بین O
Expert Solution
Step 1

Full-Time employee Cost - $105 per day

Part-time employee cost - $32 per day

Objectives and constraints are as follows:

Min Z = 105 x9 + 105 x10 + 105 x11 + 32 y9 + 32 y10 + 32 y11 + 32 y12 + 32 y1 + 32 y2 + 32 y3

Subject to:

Constraints:-

9 am to 10 am: 1 x9 + 0x10 + 0x11 + 1y9 + 0y10 + 0y11 + 0y12 + 0y1 + 0y2 + 0y3 ≥ 6 10 am to 11 am: 1x9 + 1x10 + 0x11 + 1y9 + 1y10 + 0y11 + 0y12 + 0y1 + 0y2 + 0y3 ≥ 5 11 am to Noon: 1x9 + 1x10 + 1x11 + 1y9 + 1y10 + 1y11 + 0y12 + 0y1 + 0y2 + 0y3 ≥ 7 Noon to 1 pm: 1x9 + 1x10 + 1x11 + 1y9 + 1y10 + 1y11 + 1y12 + 0y1 + 0y2 + 0y3 ≥ 11 1 pm to 2 pm: 0x9 + 1x10 + 1x11 + 0y9 + 1y10 + 1y11 + 1y12 + 1y1 + 0y2 + 0y3 ≥ 9 2 pm to 3 pm: 1x9 + 0x10 + 1x11 + 0y9 + 0y10 + 1y11 + 1y12 + 1y1 + 1y2 + y3 ≥ 7  3 pm to 4 pm: 1x9 + 1x10 + 0x11 + 0y9 + 0y10 + 0y11 + 1y12 + 1y1 + 1y2 + 1y3 ≥ 64 pm to 5 pm: 1x9 + 1x10 + 1x11 + 0y9 + 0y10 + 0y11 + 0y12 + 1y1 + 1y2 + 1y3 ≥8 5 pm to 6 pm: 0x9 + 1x10 + 1x11 + 0y9 + 0y10 + 0y11 + 0y12 + 1y1 + 1y2 + 1y3 ≥ 7 6 pm to 7 pm: 0x9 + 0x10 + 1x11 + 0y9 + 0y10 + 0y11 + 0y12 + 0y1 + 0y2 + 1y3 ≥ 9Integers: x9 ,x10 ,x11 ,y9 ,y10 ,y11 ,y12 ,y1 ,y2 ,y3 = integers

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